Question

How do you simplify `(r ^ { - 3} s ^ { 8} ) ^ { - 5}`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to eliminate the outer exponent:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(r^color(red)(-3)s^color(red)(8))^color(blue)(-5) => r^(color(red)(-3) xx color(blue)(-5))s^(color(red)(8) xx color(blue)(-5)) => r^15s^-40`

Now, use this rule of exponents to eliminate the negative exponent:

`x^color(red)(a) = 1/x^color(red)(-a)`

`r^15s^color(red)(-40) => r^15 xx 1/s^color(red)(- -40) => r^15 xx 1/s^color(red)(40) => r^15/s^40`